Susan Rice has claimed Israel's critics are biased and unjustified. Photograph: Rex Features

The senior White House adviser Susan Rice used a crucial speech on Monday to underscore the administration's commitment to Israel and dismiss critics of its military offensive in Gaza, which has claimed hundreds of civilian lives, as biased and unjustified.

In a staunch defence of Israel's response to rockets fired from the Palestinian territory controlled by Hamas, Rice was particularly critical of the United Nations human rights council, which recently voted for an inquiry into the possible war crimes violations committed by Israel.

"When countries single out Israel for unfair treatment at the UN, it isn't just a problem for Israel, it is a problem for all of us," Rice said on Monday. She added: "No country is immune from criticism, nor should it be. But when that criticism takes the form of singling out just one country, unfairly, bitterly and relentlessly, over and over and over, that is just wrong – and we all know it."

Rice, who is national security adviser to Barack Obama, expressed concern about the deaths of civilians, on both sides, and reiterated the US president's call for an immediate and unconditional humanitarian ceasefire.

The top adviser's remarks came at a critical juncture. Rice spoke shortly after Israel's prime minister, Binyamin Netanyahu, used a televised press conference to warn Israelis to prepare for a long and protracted conflict, defying international calls for a cessation of the violence.

The language used by the White House to express concern over civilian deaths has hardened slightly in recent days, as the death toll has mounted. And there have been numerous reports of friction between Washington and Jerusalem over the last 24 hours over the fallout over the failed attempt by the US secretary of state John Kerry to broker a ceasefire.

Rice said the US was "dismayed" by anonymous briefings to the Israeli press that were critical of Kerry and, she said, gave a misleading impression of his diplomatic efforts in the region. But she gave no impression the tensions between the US and Israel, which have been evident in anonymous briefings to reporters, had significantly damaged relations.

Nor did Rice give any indication the US would be bowed by the rising chorus of international concern about a conflict that has killed more than 1,080 Palestinians. The United Nations estimates more than 70% of those killed on the Palestinian side are civilians. Israel has lost 52 soldiers during the conflict and three civilians have been killed by rocket fire or mortar fire from Hamas.

Throughout the conflict the US has defended Israel's military activities while expressing concern over the death of innocent bystanders. After a brief lull in the conflict, hostilities resumed on Monday with further casualties, including nine children reportedly killed while playing in a Gaza refugee camp.

Rice's comments – the first official US statement about the conflict since Netanyahu's pledged Israel would press ahead with its offensive – were made at a hastily convened "solidarity" meeting convened by Jewish groups in Washington.

Senior Republican and Democratic political figures gave speeches at the meeting defending Israel's right to defend itself, condemning the activities of Hamas and discounting criticism of its military action as disproportionate or misguided.

"At times like this, people try to isolate Israel – but we are here to stand with Israel," said John Boehner, the Republican speaker of the House. "Not just as a broker or observer – but as a strong partner and a trusted ally." Boehner said US support for Israel "doesn't mean issuing vague, on-the-one-hand, on-the-other-hand statements", adding: "No, it means backing up our words, and showing solidarity with our friend".

Rice struck a similar tone: "Here is one thing you never have to worry about: America's support for the state of Israel." She added: "Hamas initiated this conflict. And Hamas has dragged it on."

In the portion of her remarks noting civilian suffering, Rice said: "I know we all share deep concern about the suffering and deaths of innocent people that arise from a conflict like this one, in Gaza as well as in Israel. The people of Gaza, many of whom disapprove of Hamas and suffer under its misrule, are trapped in the crossfire. The loss of children has been particularly heartbreaking."

She added: "We need to bring the violence and civilian casualties to an end and we are concerned that continued fighting could further destabilise the West Bank." However, Rice made no criticism of Israel's military operation.

Earlier, the UN security council called on both sides to implement an immediate ceasefire, expressing "grave concern" at the deteriorating situation and growing tally on civilian lives and casualties. Rice did not mention the UN resolution, which had US backing, but did express broader concern at how the international community, through the UN, treats Israel.

She singled out the vote by the UN human rights council last week in favour of an independent inquiry into alleged violations of international human rights and humanitarian law by Israel. Seventeen countries abstained during the vote, and only one country – the US – voted against.

Rice called the the UN inquiry "one-sided" and said it would "have no positive impact and should never have been created". "The United States stood with Israel, and said 'no'. We were the lone vote in the human rights council. Even our closest friends on the council abstained. It was 29 to one. But the one, as usual, was America. That is what we mean when we say: you are not alone."

Rice's remarks were briefly interrupted by a heckler, who later gave his name as Tighe Barry, 50, from Los Angeles. He said he had flown to Washington from California to attend the meeting and belonged to an organisation called Jewish Voices for Peace.

"The truth is, Israel is killing innocent people in Gaza," he yelled during Rice's speech, before he was quickly and forcefully wrestled out by security. "Stop the bombing, stop the killing, stop the hate."